Constellation based on splicing of regular rectangular pyramids and shaping design method and system thereof

Abstract

The invention discloses a constellation based on regular rectangular pyramid splicing and a shaping design method and system thereof, and belongs to the technical field of communication. The method comprises the following steps: constructing four regular rectangular pyramids by taking an original point O as a vertex to form a regular rectangular pyramid spliced structure; constructing symmetric points F, G, J, K and L of the original point O; respectively offsetting the whole constellation towards the x direction and the y direction, and enabling the geometric center of the constellation to return to the original point O; according to the geometric position of each constellation point in the constellation structure, the transmission probability of the constellation points is optimized. By optimizing the geometric structure of constellation points, the constellation gain index is improved, the minimum Euclidean distance is increased, and therefore the anti-interference capacity is effectively improved; by integrally translating constellation points, the average transmitting power is reduced, and the energy efficiency of the system is remarkably improved; and in combination with a probability shaping technology, the use probability distribution of the constellation points is optimized, the bit error rate is effectively reduced, and the transmission performance and the anti-interference capability of a communication system are improved.

Description

Technical Field

[0001] The present invention belongs to the field of communication technology, and in particular relates to a constellation based on splicing of regular tetrahedrons and a shaping design method and system thereof. Background Art

[0002] With the continuous development of communication technology, especially in the fields of optical communication and wireless communication, the demand for higher data rates and lower bit error rates is increasing. In order to achieve efficient data transmission, constellation design has become a key link in the modulation scheme. Due to the limitation of space utilization, the traditional two-dimensional constellation design is difficult to further improve the anti-noise performance and spectrum efficiency. Therefore, three-dimensional and higher-dimensional constellation structures are gradually introduced into communication systems. Compared with two-dimensional constellations, three-dimensional constellations can utilize more spatial degrees of freedom and improve the system's anti-interference ability and transmission performance by reasonably distributing constellation points. However, the complexity of three-dimensional constellation design also increases the difficulty of design and optimization, especially in improving system gain and reducing bit error rate, there are still many challenges.

[0003] In constellation design, the minimum Euclidean distance is an important indicator to measure the anti-noise performance of the constellation. A larger minimum Euclidean distance can effectively improve the anti-interference ability of the communication system and reduce the bit error rate. Although a three-dimensional constellation can increase the spatial freedom, when the number of constellation points increases, the minimum Euclidean distance between points decreases, and the reliability of the system also decreases, resulting in the constellation gain index (CFM, Constellation Figure of Merit) is still not high enough, which limits the further improvement of the communication system performance. Therefore, how to reasonably distribute the constellation points in three-dimensional space to increase the minimum Euclidean distance has become the key to improving the performance of the communication system.

[0004] Geometric Shaping (GS) is a method to improve constellation performance by optimizing the geometric position of constellation points. Through geometric shaping, the minimum Euclidean distance can be increased, thereby improving CFM. In existing three-dimensional constellation designs, although some have combined probabilistic shaping (PS) to optimize the distribution of constellation points, the overall effect is limited and CFM has not yet reached the ideal level. In addition, the lack of global optimization of the overall position of the constellation has resulted in the failure to achieve optimal system performance. Summary of the invention

[0005] In view of the deficiencies in the prior art, the object of the present invention is to provide a constellation based on the splicing of regular tetrahedrons and a shaping design method and system thereof, which solve the problems in the prior art.

[0006] The purpose of the present invention can be achieved through the following technical solutions:

[0007] A constellation shaping design method based on regular tetrahedral splicing includes the following steps:

[0008] With the origin O as the vertex, four regular tetrahedrons are constructed to form a regular tetrahedron splicing structure;

[0009] Construct the symmetric points F, G, J, K and L about the origin O;

[0010] Shift the entire constellation in the x and y directions respectively, so that the geometric center of the constellation returns to the origin O;

[0011] The transmission probability of the constellation points is optimized according to the geometric position of each constellation point in the constellation structure.

[0012] Furthermore, among the four regular tetrahedrons, the base of the first regular tetrahedron is composed of vertices A1, B1, B2 and A2, and the length of the base side and the length of each waist are both 2d; the base of the second regular tetrahedron is composed of vertices B1, B2, C2 and C1, and the length of the base side and the length of each waist are both 2d; the base of the third regular tetrahedron is composed of vertices C1, C2, D2 and D1, and the length of the base side and the length of each waist are both 2d; the base of the fourth regular tetrahedron is composed of vertices D1, D2, E2 and E1, and the length of the base side and the length of each waist are both 2d.

[0013] Furthermore, two pentagons are formed in the regular tetrahedral pyramid splicing structure: A1B1C1D1E1 and A2B2C2D2E2, the vertical distances between the origin O and the two pentagons are both d, and the distances between A1 and E1 and between A2 and E2 are both 2.1773d.

[0014] Furthermore, the symmetric point F is symmetric to the origin O about the pentagon A1B1C1D1E1, and the symmetric point G is symmetric to the origin O about the pentagon A2B2C2D2E2; and the distances between the symmetric points F and G and the origin O are both 2d.

[0015] Furthermore, the symmetric point J is symmetric to the origin O about quadrilateral A1E1E2A2, the symmetric point K is symmetric to the origin O about quadrilateral D1E1E2D2, and the symmetric point L is symmetric to the origin O about quadrilateral C1D1D2C2; and the distances between the origin O and the symmetric points K and L are both 2d.

[0016] Furthermore, the entire constellation is shifted by 0.2722d and -0.0481d in the x and y directions respectively.

[0017] Furthermore, the probability distribution of the constellation points is determined by the following formula:

[0018]

[0019] Where P x(x) represents the probability distribution of constellation point x, v is a non-negative scaling factor used to adjust the degree of constellation shaping and the information entropy of the modulation scheme. When v = 0, the probability distribution of the constellation points is uniform and the information entropy reaches the maximum value. When v>0, the probability distribution gradually converges to the direction of low information entropy; |x| 2 represents the power of constellation point x; is a normalization factor used to ensure that the sum of the probabilities of all constellation points is 1; X is the set of all constellation points; x represents a constellation point in the current constellation diagram; x′∈X represents a constellation point in the constellation point set X, which is used for normalization calculation.

[0020] A constellation shaping design system based on regular tetrahedral pyramid splicing, comprising:

[0021] Regular tetrahedron building module: With the origin O as the vertex, four regular tetrahedrons are constructed to form a regular tetrahedron splicing structure;

[0022] Symmetric point construction module: construct symmetrical points F, G, J, K and L of the origin O;

[0023] Constellation translation module: shift the entire constellation in the x and y directions respectively, so that the geometric center of the constellation returns to the origin O;

[0024] And, the probability shaping module: optimizes the transmission probability of the constellation points according to the geometric position of each constellation point in the constellation structure.

[0025] A constellation based on splicing of regular tetrahedrons is designed using the above-mentioned constellation shaping design method based on splicing of regular tetrahedrons.

[0026] A computer storage medium stores a readable program, which can execute the above-mentioned constellation shaping design method based on regular tetrahedral splicing when the program is running.

[0027] Beneficial effects of the present invention:

[0028] 1. The present invention improves the constellation gain index and the minimum Euclidean distance by optimizing the geometric structure of the constellation points, thereby effectively improving the anti-interference capability.

[0029] 2. By overall shifting the constellation points, the average transmit power is reduced and the energy efficiency of the system is significantly improved.

[0030] 3. Combined with probability shaping technology, the probability distribution of constellation points is optimized, which effectively reduces the bit error rate and improves the transmission performance and anti-interference ability of the communication system. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0032] Figure 1 It is a flow chart of the design of the regular tetrahedral splicing constellation structure of the present invention;

[0033] Figure 2 It is a regular tetrahedral splicing constellation mapping diagram of the present invention. DETAILED DESCRIPTION

[0034] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0035] Example 1

[0036] like Figure 1 As shown, a constellation design method based on regular tetrahedron splicing includes the following steps:

[0037] S1, construct a regular tetrahedral pyramid splicing structure;

[0038] like Figure 1 As shown in (a), four regular tetrahedrons are constructed with the origin O as the vertex. The base of the first regular tetrahedron is composed of vertices A1, B1, B2 and A2, and the length of the base side and the length of each waist are 2d. Similarly, the other three regular tetrahedrons are also formed by four different vertices and the origin O. The side surfaces are connected to each other and together form a regular tetrahedron splicing structure around the origin O. For the other three regular tetrahedrons, their specific structures are:

[0039] The base of the second regular tetrahedron is composed of vertices B1, B2, C2 and C1, and the length of the base side and the length of each waist are both 2d; the base of the third regular tetrahedron is composed of vertices C1, C2, D2 and D1, and the length of the base side and the length of each waist are both 2d; the base of the fourth regular tetrahedron is composed of vertices D1, D2, E2 and E1, and the length of the base side and the length of each waist are both 2d.

[0040] Through this geometric layout, two pentagons are formed: A1B1C1D1E1 and A2B2C2D2E2. These two pentagons are not standard regular pentagons. The perpendicular distance between the origin O and the two pentagons is d, and the distance between A1 and E1 and between A2 and E2 is 2.1773d.

[0041] S2, construct the symmetric points F and G of the origin O;

[0042] like Figure 1 As shown in (b), for the two pentagons A1B1C1D1E1 and A2B2C2D2E2, construct the symmetric points F and G of the origin O. The distance between points F and G and the origin O is 2d.

[0043] S3, construct the symmetric points J, K, L of point O;

[0044] like Figure 1 As shown in (c), the symmetric points J, K and L of the origin O relative to quadrilateral A1E1E2A2, quadrilateral D1E1E2D2 and quadrilateral C1D1D2C2 are constructed respectively. After the construction, the distance between point O and points K and L is 2d.

[0045] S4, shift the entire constellation in the x and y directions by 0.2722d and -0.0481d respectively, so that the geometric center of the constellation returns to the origin O.

[0046] The geometric shaping design of the constellation is completed through S1-S4. Through the above geometric construction, the number of point pairs that meet the minimum Euclidean distance is maximized, with a total of 47 pairs, ensuring that the constellation points are evenly distributed in the three-dimensional space, reducing the overall average power, thereby greatly improving the constellation gain index CFM.

[0047] The calculation formula of the known constellation gain index is:

[0048]

[0049] Among them, d min is the minimum Euclidean distance between constellation points, P avg is the average power of the constellation points, calculated as the average of the squares of the distances from all constellation points to the origin.

[0050] It can be calculated that the CFM of the traditional three-dimensional constellation with a regular hexahedron as the primitive is 0.4726, and the CFM of the regular tetrahedron splicing constellation structure designed by the present invention before the overall translation is 0.8981, and the CFM after the translation is 0.9138. Compared with the traditional three-dimensional constellation with a regular hexahedron primitive, it is improved by 0.4412, and at the same power, it can greatly reduce the bit error rate of the communication system.

[0051] After determining the positions of the 16 constellation points, the present invention maps the constellation points, mapping the bits carrying digital information into 16 serial number sequences, where one serial number contains 4 bits. Since there are more adjacent point pairs in the constellation designed by the present invention, the Hamming distance of any adjacent symbols that cannot be completely Gray-mapped is 1, so the total Hamming distance of the system can only be minimized to make the sum of the differences in adjacent bits of the entire system as small as possible, and the bit error rate can be minimized under the same symbol error rate. The system of the present invention also uses probability shaping, and the probability of points in the constellation that are close to the origin is greater than that of points that are far away. Therefore, priority is assigned according to distance, and the Hamming distance of the center point is minimized first. The mapping rules are shown in Tables 1 and Figure 2 shown.

[0052] Table 1 Constellation point coordinates and mapping bits

[0053]

[0054] S5, optimizing the transmission probability of the constellation points according to the geometric positions of the constellation points in the constellation structure, and realizing probability shaping of the constellation points;

[0055] After completing the geometric shaping of the three-dimensional constellation, the present invention further optimizes the transmission probability of the constellation points through the probability shaping technology to reduce the bit error rate and improve the transmission performance of the system. Specifically, for each constellation point in the three-dimensional constellation structure, the impact of the constellation point on the overall system performance is first evaluated based on its geometric position in the three-dimensional space. In order to better improve the system energy efficiency and increase communication reliability, the present invention selectively assigns a higher transmission probability to the constellation points close to the origin, thereby effectively reducing the bit error rate.

[0056] The transmission probability distribution of the constellation points is determined by the following formula:

[0057]

[0058] Among them, P x (x) represents the probability distribution of constellation point x. v is a non-negative scaling factor used to adjust the degree of constellation shaping and the information entropy of the modulation scheme. When v = 0, the probability distribution of the constellation points is uniform and the information entropy reaches the maximum value. When v>0, the probability distribution gradually converges to the direction of low information entropy. |x| 2 represents the power of constellation point x. is a normalization factor used to ensure that the sum of all constellation point probabilities is 1. X is the set of all constellation points. x represents a constellation point in the current constellation diagram. x′∈X represents a constellation point in the constellation point set X, which is used for normalization calculation.

[0059] The following table lists the information entropy and constellation gain index corresponding to different ν values.

[0060] Table 2 The influence of different probability shaping parameters on constellation information entropy and gain index

[0061]

[0062] As can be seen from Table 2, through probability shaping, the transmission probability of the constellation points has been reasonably optimized. Compared with the constellation without probability shaping, the system after probability shaping has higher reliability and anti-interference ability. This optimization ensures that the system is closer to the Shannon limit under the same power conditions, meeting the needs of modern optical communication and wireless communication systems for efficient and reliable data transmission.

[0063] Based on similar inventive concepts, an embodiment of the present invention further provides a computer storage medium storing a readable program, which can execute the above-mentioned constellation shaping design method based on regular tetrahedral pyramid splicing when the program is running.

[0064] Based on similar inventive concepts, an embodiment of the present invention provides an electronic device, comprising: a processor, a memory, a communication interface and a communication bus, wherein the processor, the memory and the communication interface communicate with each other through the communication bus;

[0065] The memory is used to store at least one executable instruction, and the executable instruction enables the processor to perform operations corresponding to the above-mentioned constellation shaping design method based on regular tetrahedral splicing.

[0066] Based on similar inventive concepts, an embodiment of the present invention further provides a computer program product, including computer instructions, which instruct a computing device to execute operations corresponding to the above-mentioned constellation shaping design method based on regular tetrahedral splicing.

[0067] Example 2

[0068] In this embodiment, a constellation shaping design system based on regular tetrahedron splicing is proposed, which specifically includes:

[0069] Regular tetrahedron building module: With the origin O as the vertex, four regular tetrahedrons are constructed to form a regular tetrahedron splicing structure;

[0070] Symmetric point construction module: construct symmetrical points F, G, J, K and L of the origin O;

[0071] Constellation translation module: shift the entire constellation in the x and y directions respectively, so that the geometric center of the constellation returns to the origin O;

[0072] And, the probability shaping module: optimizes the transmission probability of the constellation points according to the geometric position of each constellation point in the constellation structure.

[0073] The method of the present invention may be implemented in hardware, firmware, or as software or computer code that may be stored in a recording medium (such as a CDROM, RAM, floppy disk, hard disk, or magneto-optical disk), or as computer code that is originally stored in a remote recording medium or a non-temporary machine-readable medium downloaded over a network and will be stored in a local recording medium, so that the method described herein may be stored in such software processing on a recording medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware (such as an ASIC or FPGA). It is understood that a computer, processor, microprocessor controller, or programmable hardware includes a storage component (e.g., RAM, ROM, flash memory, etc.) that can store or receive software or computer code, and when the software or computer code is accessed and executed by a computer, processor, or hardware, the method described herein is implemented. In addition, when a general-purpose computer accesses the code for implementing the method shown herein, the execution of the code converts the general-purpose computer into a dedicated computer for executing the method shown herein.

[0074] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of the present invention to be protected.

Claims

1. A constellation shaping design method based on regular tetrahedral pyramid splicing, characterized in that: The following steps are involved: With the origin O as the vertex, four regular tetrahedrons are constructed to form a regular tetrahedron splicing structure; Construct the symmetric points F, G, J, K and L about the origin O; Shift the entire constellation in the x and y directions respectively, so that the geometric center of the constellation returns to the origin O; The transmission probability of the constellation points is optimized according to the geometric position of each constellation point in the constellation structure.

2. The constellation shaping design method based on regular tetrahedral pyramid splicing according to claim 1, characterized in that: Among the four regular tetrahedrons, the base of the first regular tetrahedron is composed of vertices A1, B1, B2 and A2, and the length of the base side and the length of each waist are both 2d; the base of the second regular tetrahedron is composed of vertices B1, B2, C2 and C1, and the length of the base side and the length of each waist are both 2d; the base of the third regular tetrahedron is composed of vertices C1, C2, D2 and D1, and the length of the base side and the length of each waist are both 2d; the base of the fourth regular tetrahedron is composed of vertices D1, D2, E2 and E1, and the length of the base side and the length of each waist are both 2d.

3. The constellation shaping design method based on regular tetrahedral pyramid splicing according to claim 2, characterized in that: Two pentagons are formed in the regular tetrahedral pyramid splicing structure: A1B1C1D1E1 and A2B2C2D2E2. The vertical distances between the origin O and the two pentagons are both d, and the distances between A1 and E1 and between A2 and E2 are both 2.1773d.

4. The constellation shaping design method based on regular tetrahedral pyramid splicing according to claim 3, characterized in that: The symmetric point F is symmetric to the origin O about the pentagon A1B1C1D1E1, and the symmetric point G is symmetric to the origin O about the pentagon A2B2C2D2E2; and the distances between the symmetric points F and G and the origin O are both 2d.

5. The constellation shaping design method based on regular tetrahedral pyramid splicing according to claim 3, characterized in that: The symmetric point J is symmetric with the origin O about quadrilateral A1E1E2A2, the symmetric point K is symmetric with the origin O about quadrilateral D1E1E2D2, and the symmetric point L is symmetric with the origin O about quadrilateral C1D1D2C2; and the distance between the origin O and the symmetric points K and L is 2d.

6. The constellation shaping design method based on regular tetrahedral pyramid splicing according to claim 1, characterized in that: The entire constellation is shifted by 0.2722d and -0.0481d in the x and y directions respectively.

7. The constellation shaping design method based on regular tetrahedral pyramid splicing according to claim 1, characterized in that: The probability distribution of the constellation points is determined by the following formula: Where P x (x) represents the probability distribution of constellation point x, v is a non-negative scaling factor used to adjust the degree of constellation shaping and the information entropy of the modulation scheme. When v = 0, the probability distribution of the constellation points is uniform and the information entropy reaches the maximum value. When v>0, the probability distribution gradually converges to the direction of low information entropy; |x| 2 represents the power of constellation point x; is a normalization factor used to ensure that the sum of the probabilities of all constellation points is 1; X is the set of all constellation points; x represents a constellation point in the current constellation diagram; x′∈X represents a constellation point in the constellation point set X, which is used for normalization calculation.

8. A constellation shaping design system based on regular tetrahedral pyramid splicing, characterized in that: include: Regular tetrahedron building module: With the origin O as the vertex, four regular tetrahedrons are constructed to form a regular tetrahedron splicing structure; Symmetric point construction module: construct symmetrical points F, G, J, K and L of the origin O; Constellation translation module: shift the entire constellation in the x and y directions respectively, so that the geometric center of the constellation returns to the origin O; And, the probability shaping module: optimizes the transmission probability of the constellation points according to the geometric position of each constellation point in the constellation structure.

9. A constellation based on regular tetrahedron splicing, characterized in that: The constellation shaping design method based on splicing of regular tetrahedrons as described in any one of claims 1 to 7 is adopted for design.

10. A computer storage medium storing a readable program, characterized in that: When the program is running, it can execute the constellation shaping design method based on regular tetrahedral splicing as described in any one of claims 1 to 7.

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